Aircraft: RV-8
Phase of flight: Landing; Final Approach; Initial Approach
Anomaly: Conflict Airborne Conflict; Deviation / Discrepancy - Procedural Published Material / Policy

I was leading a flight of 2 into ZZZ.Our flight was following a flight of 3 Aircraft on a left downwind for Runway 34 at ZZZ. Since the [flight of 3] were extending the downwind for individual spacing I elected to fly the overhead pattern for my flight to prevent spacing problems and expedite landing.On downwind; 90 to initial (Base turn at pattern altitude) and initial I announced our intention to fly an overhead pattern for full stop landings.On short initial (just prior to pitching out for the inside downwind Aircraft Y called on the 45 to the outside downwind. On inside downwind just as I was rolling into a left base turn to final my wingman alerted me to the Aircraft Y coming up abeam me on the outside downwind. I noted that Aircraft Y was at a higher speed and was starting a left base from the outside downwind.Due to the position and closure of the Aircraft Y I made a call to alert the pilot that there were 2 aircraft ahead of him in the base turn. The Aircraft Y pilot response was 'I am really pissed off; you two cut me off'. As we continued our turn to final my wingman recommended Aircraft Y's pilot to check the FARs. His response was 'I don't give a S**T about the FARs'. Aircraft Y's pilot also accused us of being unprofessional and creating a hazard.On short final I announced that my flight would be going around (this would let the Aircraft Y land unimpeded); Aircraft Y announced that he was already going around so both my wingman and I landed to prevent an unsafe situation from developing due to 3 aircraft going around in close proximity.After landing Aircraft Y flew a touch and go then landed to taxi by and record our N numbers.The 3 pilots that landed before us witnessed the event and have volunteered to submit statements as needed.There appear to be several educational points associated with this event.1. Situational awareness and aeronautical decision making: When Aircraft Y was alerted to our presence he could have easily made an extension of his downwind for spacing as there was no traffic behind him. This would have eliminated any spacing issues.2. Professionalism: Although my wingman and I were accused of being unprofessional Aircraft Y's pilots conduct was noted by witnesses as a case of 'Road Rage' in the air and potential anger management issues.3. Overhead Traffic Pattern: While military pilots are trained in flying overhead traffic patterns many general aviation pilots are unfamiliar even though it is covered in the Airman's Information Manual. When executed correctly the overhead pattern is more efficient and safer for landing numerous aircraft as opposed to stringing out the downwind pattern for spacing.Formation flying groups are operating all across the country so overhead patterns would appear to be a good topic for FAA Safety Seminars.Both my wingman and I are members of 2 formation flying groups that perform in air shows and special events. When we train new flight leads the group's emphasis is placed on being courteous and considerate of other pilots in the traffic pattern. Some of the techniques taught to new flight leads include:1. Adjusting the outside downwind to avoid conflicts.2. Delaying the overhead break when an airplane is past midfield on the outside downwind.3. Taking the flight straight through initial and back to the outside downwind when there are numerous other aircraft trying to land.4. Breaking the formation out of the traffic pattern to avoid a conflict. Lead RV8 Pilot in a flight of two; while accomplishing an overhead pattern; reported an airborne conflict with another light aircraft entering the rectangular traffic pattern at a non-towered airport.